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org.apache.commons.math3.linear</FONT>
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Class MatrixUtils</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.linear.MatrixUtils</B>
</PRE>
<HR>
<DL>
<DT><PRE>public class <B>MatrixUtils</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></DL>
</PRE>

<P>
A collection of static methods that operate on or return matrices.
<P>

<P>
<DL>
<DT><B>Version:</B></DT>
  <DD>$Id: MatrixUtils.java 1449528 2013-02-24 19:06:20Z luc $</DD>
</DL>
<HR>

<P>
<!-- =========== FIELD SUMMARY =========== -->

<A NAME="field_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Field Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrixFormat.html" title="class in org.apache.commons.math3.linear">RealMatrixFormat</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#DEFAULT_FORMAT">DEFAULT_FORMAT</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The default format for <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> objects.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrixFormat.html" title="class in org.apache.commons.math3.linear">RealMatrixFormat</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#OCTAVE_FORMAT">OCTAVE_FORMAT</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A format for <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> objects compatible with octave.</TD>
</TR>
</TABLE>
&nbsp;
<!-- ========== METHOD SUMMARY =========== -->

<A NAME="method_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Method Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#bigFractionMatrixToRealMatrix(org.apache.commons.math3.linear.FieldMatrix)">bigFractionMatrixToRealMatrix</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction">BigFraction</A>&gt;&nbsp;m)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Convert a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A>/<A HREF="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><CODE>BigFraction</CODE></A> matrix to a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#blockInverse(org.apache.commons.math3.linear.RealMatrix, int)">blockInverse</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;m,
             int&nbsp;splitIndex)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the inverse of the given matrix by splitting it into
 4 sub-matrices.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkAdditionCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)">checkAdditionCompatible</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;left,
                        <A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;right)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if matrices are addition compatible.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkColumnIndex(org.apache.commons.math3.linear.AnyMatrix, int)">checkColumnIndex</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                 int&nbsp;column)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if a column index is valid.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int, int)">checkMatrixIndex</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                 int&nbsp;row,
                 int&nbsp;column)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if matrix indices are valid.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkMultiplicationCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)">checkMultiplicationCompatible</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;left,
                              <A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;right)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if matrices are multiplication compatible</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkRowIndex(org.apache.commons.math3.linear.AnyMatrix, int)">checkRowIndex</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
              int&nbsp;row)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if a row index is valid.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkSubMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int[], int[])">checkSubMatrixIndex</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                    int[]&nbsp;selectedRows,
                    int[]&nbsp;selectedColumns)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if submatrix ranges indices are valid.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkSubMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int, int, int, int)">checkSubMatrixIndex</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                    int&nbsp;startRow,
                    int&nbsp;endRow,
                    int&nbsp;startColumn,
                    int&nbsp;endColumn)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if submatrix ranges indices are valid.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkSubtractionCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)">checkSubtractionCompatible</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;left,
                           <A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;right)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if matrices are subtraction compatible</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkSymmetric(org.apache.commons.math3.linear.RealMatrix, double)">checkSymmetric</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
               double&nbsp;eps)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Checks whether a matrix is symmetric.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="0" SUMMARY="">
<TR ALIGN="right" VALIGN="">
<TD NOWRAP><FONT SIZE="-1">
<CODE>&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; 
<BR>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt;</CODE></FONT></TD>
</TR>
</TABLE>
</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createColumnFieldMatrix(T[])">createColumnFieldMatrix</A></B>(T[]&nbsp;columnData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a column <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> using the data from the input
 array.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createColumnRealMatrix(double[])">createColumnRealMatrix</A></B>(double[]&nbsp;columnData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a column <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> using the data from the input
 array.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="0" SUMMARY="">
<TR ALIGN="right" VALIGN="">
<TD NOWRAP><FONT SIZE="-1">
<CODE>&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; 
<BR>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt;</CODE></FONT></TD>
</TR>
</TABLE>
</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldDiagonalMatrix(T[])">createFieldDiagonalMatrix</A></B>(T[]&nbsp;diagonal)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a diagonal matrix with specified elements.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="0" SUMMARY="">
<TR ALIGN="right" VALIGN="">
<TD NOWRAP><FONT SIZE="-1">
<CODE>&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; 
<BR>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt;</CODE></FONT></TD>
</TR>
</TABLE>
</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldIdentityMatrix(org.apache.commons.math3.Field, int)">createFieldIdentityMatrix</A></B>(<A HREF="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</A>&lt;T&gt;&nbsp;field,
                          int&nbsp;dimension)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns <code>dimension x dimension</code> identity matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="0" SUMMARY="">
<TR ALIGN="right" VALIGN="">
<TD NOWRAP><FONT SIZE="-1">
<CODE>&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; 
<BR>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt;</CODE></FONT></TD>
</TR>
</TABLE>
</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldMatrix(org.apache.commons.math3.Field, int, int)">createFieldMatrix</A></B>(<A HREF="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</A>&lt;T&gt;&nbsp;field,
                  int&nbsp;rows,
                  int&nbsp;columns)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> with specified dimensions.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="0" SUMMARY="">
<TR ALIGN="right" VALIGN="">
<TD NOWRAP><FONT SIZE="-1">
<CODE>&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; 
<BR>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt;</CODE></FONT></TD>
</TR>
</TABLE>
</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldMatrix(T[][])">createFieldMatrix</A></B>(T[][]&nbsp;data)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> whose entries are the the values in the
 the input array.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="0" SUMMARY="">
<TR ALIGN="right" VALIGN="">
<TD NOWRAP><FONT SIZE="-1">
<CODE>&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; 
<BR>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear">FieldVector</A>&lt;T&gt;</CODE></FONT></TD>
</TR>
</TABLE>
</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldVector(T[])">createFieldVector</A></B>(T[]&nbsp;data)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a <A HREF="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldVector</CODE></A> using the data from the input array.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealDiagonalMatrix(double[])">createRealDiagonalMatrix</A></B>(double[]&nbsp;diagonal)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a diagonal matrix with specified elements.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealIdentityMatrix(int)">createRealIdentityMatrix</A></B>(int&nbsp;dimension)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns <code>dimension x dimension</code> identity matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealMatrix(double[][])">createRealMatrix</A></B>(double[][]&nbsp;data)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> whose entries are the the values in the
 the input array.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealMatrix(int, int)">createRealMatrix</A></B>(int&nbsp;rows,
                 int&nbsp;columns)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> with specified dimensions.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealVector(double[])">createRealVector</A></B>(double[]&nbsp;data)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> using the data from the input array.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="0" SUMMARY="">
<TR ALIGN="right" VALIGN="">
<TD NOWRAP><FONT SIZE="-1">
<CODE>&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; 
<BR>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt;</CODE></FONT></TD>
</TR>
</TABLE>
</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRowFieldMatrix(T[])">createRowFieldMatrix</A></B>(T[]&nbsp;rowData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Create a row <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> using the data from the input
 array.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRowRealMatrix(double[])">createRowRealMatrix</A></B>(double[]&nbsp;rowData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Create a row <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> using the data from the input
 array.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#deserializeRealMatrix(java.lang.Object, java.lang.String, java.io.ObjectInputStream)">deserializeRealMatrix</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>&nbsp;instance,
                      <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A>&nbsp;fieldName,
                      <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/ObjectInputStream.html?is-external=true" title="class or interface in java.io">ObjectInputStream</A>&nbsp;ois)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Deserialize  a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> field in a class.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#deserializeRealVector(java.lang.Object, java.lang.String, java.io.ObjectInputStream)">deserializeRealVector</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>&nbsp;instance,
                      <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A>&nbsp;fieldName,
                      <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/ObjectInputStream.html?is-external=true" title="class or interface in java.io">ObjectInputStream</A>&nbsp;ois)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Deserialize  a <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> field in a class.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#fractionMatrixToRealMatrix(org.apache.commons.math3.linear.FieldMatrix)">fractionMatrixToRealMatrix</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/fraction/Fraction.html" title="class in org.apache.commons.math3.fraction">Fraction</A>&gt;&nbsp;m)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Convert a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A>/<A HREF="../../../../../org/apache/commons/math3/fraction/Fraction.html" title="class in org.apache.commons.math3.fraction"><CODE>Fraction</CODE></A> matrix to a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#isSymmetric(org.apache.commons.math3.linear.RealMatrix, double)">isSymmetric</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
            double&nbsp;eps)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Checks whether a matrix is symmetric.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#serializeRealMatrix(org.apache.commons.math3.linear.RealMatrix, java.io.ObjectOutputStream)">serializeRealMatrix</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
                    <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/ObjectOutputStream.html?is-external=true" title="class or interface in java.io">ObjectOutputStream</A>&nbsp;oos)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Serialize a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#serializeRealVector(org.apache.commons.math3.linear.RealVector, java.io.ObjectOutputStream)">serializeRealVector</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;vector,
                    <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/ObjectOutputStream.html?is-external=true" title="class or interface in java.io">ObjectOutputStream</A>&nbsp;oos)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Serialize a <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#solveLowerTriangularSystem(org.apache.commons.math3.linear.RealMatrix, org.apache.commons.math3.linear.RealVector)">solveLowerTriangularSystem</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;rm,
                           <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solve  a  system of composed of a Lower Triangular Matrix
 <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#solveUpperTriangularSystem(org.apache.commons.math3.linear.RealMatrix, org.apache.commons.math3.linear.RealVector)">solveUpperTriangularSystem</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;rm,
                           <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solver a  system composed  of an Upper Triangular Matrix
 <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<P>

<!-- ============ FIELD DETAIL =========== -->

<A NAME="field_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Field Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="DEFAULT_FORMAT"><!-- --></A><H3>
DEFAULT_FORMAT</H3>
<PRE>
public static final <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrixFormat.html" title="class in org.apache.commons.math3.linear">RealMatrixFormat</A> <B>DEFAULT_FORMAT</B></PRE>
<DL>
<DD>The default format for <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> objects.
<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DL>
<HR>

<A NAME="OCTAVE_FORMAT"><!-- --></A><H3>
OCTAVE_FORMAT</H3>
<PRE>
public static final <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrixFormat.html" title="class in org.apache.commons.math3.linear">RealMatrixFormat</A> <B>OCTAVE_FORMAT</B></PRE>
<DL>
<DD>A format for <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> objects compatible with octave.
<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DL>

<!-- ============ METHOD DETAIL ========== -->

<A NAME="method_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Method Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="createRealMatrix(int, int)"><!-- --></A><H3>
createRealMatrix</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>createRealMatrix</B>(int&nbsp;rows,
                                          int&nbsp;columns)</PRE>
<DL>
<DD>Returns a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> with specified dimensions.
 <p>The type of matrix returned depends on the dimension. Below
 2<sup>12</sup> elements (i.e. 4096 elements or 64&times;64 for a
 square matrix) which can be stored in a 32kB array, a <A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear"><CODE>Array2DRowRealMatrix</CODE></A> instance is built. Above this threshold a <A HREF="../../../../../org/apache/commons/math3/linear/BlockRealMatrix.html" title="class in org.apache.commons.math3.linear"><CODE>BlockRealMatrix</CODE></A> instance is built.</p>
 <p>The matrix elements are all set to 0.0.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>rows</CODE> - number of rows of the matrix<DD><CODE>columns</CODE> - number of columns of the matrix
<DT><B>Returns:</B><DD>RealMatrix with specified dimensions<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealMatrix(double[][])"><CODE>createRealMatrix(double[][])</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="createFieldMatrix(org.apache.commons.math3.Field, int, int)"><!-- --></A><H3>
createFieldMatrix</H3>
<PRE>
public static &lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt; <B>createFieldMatrix</B>(<A HREF="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</A>&lt;T&gt;&nbsp;field,
                                                                           int&nbsp;rows,
                                                                           int&nbsp;columns)</PRE>
<DL>
<DD>Returns a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> with specified dimensions.
 <p>The type of matrix returned depends on the dimension. Below
 2<sup>12</sup> elements (i.e. 4096 elements or 64&times;64 for a
 square matrix), a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> instance is built. Above
 this threshold a <A HREF="../../../../../org/apache/commons/math3/linear/BlockFieldMatrix.html" title="class in org.apache.commons.math3.linear"><CODE>BlockFieldMatrix</CODE></A> instance is built.</p>
 <p>The matrix elements are all set to field.getZero().</p>
<P>
<DD><DL>
<DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements<DT><B>Parameters:</B><DD><CODE>field</CODE> - field to which the matrix elements belong<DD><CODE>rows</CODE> - number of rows of the matrix<DD><CODE>columns</CODE> - number of columns of the matrix
<DT><B>Returns:</B><DD>FieldMatrix with specified dimensions<DT><B>Since:</B></DT>
  <DD>2.0</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldMatrix(T[][])"><CODE>createFieldMatrix(FieldElement[][])</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="createRealMatrix(double[][])"><!-- --></A><H3>
createRealMatrix</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>createRealMatrix</B>(double[][]&nbsp;data)
                                   throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                                          <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                                          <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></PRE>
<DL>
<DD>Returns a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> whose entries are the the values in the
 the input array.
 <p>The type of matrix returned depends on the dimension. Below
 2<sup>12</sup> elements (i.e. 4096 elements or 64&times;64 for a
 square matrix) which can be stored in a 32kB array, a <A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear"><CODE>Array2DRowRealMatrix</CODE></A> instance is built. Above this threshold a <A HREF="../../../../../org/apache/commons/math3/linear/BlockRealMatrix.html" title="class in org.apache.commons.math3.linear"><CODE>BlockRealMatrix</CODE></A> instance is built.</p>
 <p>The input array is copied, not referenced.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>data</CODE> - input array
<DT><B>Returns:</B><DD>RealMatrix containing the values of the array
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>data</code> is not rectangular (not all rows have the same length).
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if a row or column is empty.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if either <code>data</code> or <code>data[0]</code>
 is <code>null</code>.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>data</code> is not rectangular.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealMatrix(int, int)"><CODE>createRealMatrix(int, int)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="createFieldMatrix(org.apache.commons.math3.FieldElement[][])"><!-- --></A><A NAME="createFieldMatrix(T[][])"><!-- --></A><H3>
createFieldMatrix</H3>
<PRE>
public static &lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt; <B>createFieldMatrix</B>(T[][]&nbsp;data)
                                                                throws <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                                                                       <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A>,
                                                                       <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Returns a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> whose entries are the the values in the
 the input array.
 <p>The type of matrix returned depends on the dimension. Below
 2<sup>12</sup> elements (i.e. 4096 elements or 64&times;64 for a
 square matrix), a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> instance is built. Above
 this threshold a <A HREF="../../../../../org/apache/commons/math3/linear/BlockFieldMatrix.html" title="class in org.apache.commons.math3.linear"><CODE>BlockFieldMatrix</CODE></A> instance is built.</p>
 <p>The input array is copied, not referenced.</p>
<P>
<DD><DL>
<DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements<DT><B>Parameters:</B><DD><CODE>data</CODE> - input array
<DT><B>Returns:</B><DD>a matrix containing the values of the array.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>data</code> is not rectangular (not all rows have the same length).
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if a row or column is empty.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if either <code>data</code> or <code>data[0]</code>
 is <code>null</code>.<DT><B>Since:</B></DT>
  <DD>2.0</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldMatrix(org.apache.commons.math3.Field, int, int)"><CODE>createFieldMatrix(Field, int, int)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="createRealIdentityMatrix(int)"><!-- --></A><H3>
createRealIdentityMatrix</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>createRealIdentityMatrix</B>(int&nbsp;dimension)</PRE>
<DL>
<DD>Returns <code>dimension x dimension</code> identity matrix.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>dimension</CODE> - dimension of identity matrix to generate
<DT><B>Returns:</B><DD>identity matrix
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if dimension is not positive<DT><B>Since:</B></DT>
  <DD>1.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="createFieldIdentityMatrix(org.apache.commons.math3.Field, int)"><!-- --></A><H3>
createFieldIdentityMatrix</H3>
<PRE>
public static &lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt; <B>createFieldIdentityMatrix</B>(<A HREF="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</A>&lt;T&gt;&nbsp;field,
                                                                                   int&nbsp;dimension)</PRE>
<DL>
<DD>Returns <code>dimension x dimension</code> identity matrix.
<P>
<DD><DL>
<DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements<DT><B>Parameters:</B><DD><CODE>field</CODE> - field to which the elements belong<DD><CODE>dimension</CODE> - dimension of identity matrix to generate
<DT><B>Returns:</B><DD>identity matrix
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if dimension is not positive<DT><B>Since:</B></DT>
  <DD>2.0</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="createRealDiagonalMatrix(double[])"><!-- --></A><H3>
createRealDiagonalMatrix</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>createRealDiagonalMatrix</B>(double[]&nbsp;diagonal)</PRE>
<DL>
<DD>Returns a diagonal matrix with specified elements.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>diagonal</CODE> - diagonal elements of the matrix (the array elements
 will be copied)
<DT><B>Returns:</B><DD>diagonal matrix<DT><B>Since:</B></DT>
  <DD>2.0</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="createFieldDiagonalMatrix(org.apache.commons.math3.FieldElement[])"><!-- --></A><A NAME="createFieldDiagonalMatrix(T[])"><!-- --></A><H3>
createFieldDiagonalMatrix</H3>
<PRE>
public static &lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt; <B>createFieldDiagonalMatrix</B>(T[]&nbsp;diagonal)</PRE>
<DL>
<DD>Returns a diagonal matrix with specified elements.
<P>
<DD><DL>
<DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements<DT><B>Parameters:</B><DD><CODE>diagonal</CODE> - diagonal elements of the matrix (the array elements
 will be copied)
<DT><B>Returns:</B><DD>diagonal matrix<DT><B>Since:</B></DT>
  <DD>2.0</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="createRealVector(double[])"><!-- --></A><H3>
createRealVector</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>createRealVector</B>(double[]&nbsp;data)
                                   throws <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A>,
                                          <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Creates a <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> using the data from the input array.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>data</CODE> - the input data
<DT><B>Returns:</B><DD>a data.length RealVector
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if <code>data</code> is empty.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>data</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="createFieldVector(org.apache.commons.math3.FieldElement[])"><!-- --></A><A NAME="createFieldVector(T[])"><!-- --></A><H3>
createFieldVector</H3>
<PRE>
public static &lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; <A HREF="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear">FieldVector</A>&lt;T&gt; <B>createFieldVector</B>(T[]&nbsp;data)
                                                                throws <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A>,
                                                                       <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                                                                       <A HREF="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</A></PRE>
<DL>
<DD>Creates a <A HREF="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldVector</CODE></A> using the data from the input array.
<P>
<DD><DL>
<DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements<DT><B>Parameters:</B><DD><CODE>data</CODE> - the input data
<DT><B>Returns:</B><DD>a data.length FieldVector
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if <code>data</code> is empty.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>data</code> is <code>null</code>.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</A></CODE> - if <code>data</code> has 0 elements</DL>
</DD>
</DL>
<HR>

<A NAME="createRowRealMatrix(double[])"><!-- --></A><H3>
createRowRealMatrix</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>createRowRealMatrix</B>(double[]&nbsp;rowData)
                                      throws <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A>,
                                             <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Create a row <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> using the data from the input
 array.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>rowData</CODE> - the input row data
<DT><B>Returns:</B><DD>a 1 x rowData.length RealMatrix
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if <code>rowData</code> is empty.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>rowData</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="createRowFieldMatrix(org.apache.commons.math3.FieldElement[])"><!-- --></A><A NAME="createRowFieldMatrix(T[])"><!-- --></A><H3>
createRowFieldMatrix</H3>
<PRE>
public static &lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt; <B>createRowFieldMatrix</B>(T[]&nbsp;rowData)
                                                                   throws <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A>,
                                                                          <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Create a row <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> using the data from the input
 array.
<P>
<DD><DL>
<DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements<DT><B>Parameters:</B><DD><CODE>rowData</CODE> - the input row data
<DT><B>Returns:</B><DD>a 1 x rowData.length FieldMatrix
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if <code>rowData</code> is empty.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>rowData</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="createColumnRealMatrix(double[])"><!-- --></A><H3>
createColumnRealMatrix</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>createColumnRealMatrix</B>(double[]&nbsp;columnData)
                                         throws <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A>,
                                                <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Creates a column <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> using the data from the input
 array.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>columnData</CODE> - the input column data
<DT><B>Returns:</B><DD>a columnData x 1 RealMatrix
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if <code>columnData</code> is empty.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>columnData</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="createColumnFieldMatrix(org.apache.commons.math3.FieldElement[])"><!-- --></A><A NAME="createColumnFieldMatrix(T[])"><!-- --></A><H3>
createColumnFieldMatrix</H3>
<PRE>
public static &lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt; <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;T&gt; <B>createColumnFieldMatrix</B>(T[]&nbsp;columnData)
                                                                      throws <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A>,
                                                                             <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Creates a column <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A> using the data from the input
 array.
<P>
<DD><DL>
<DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements<DT><B>Parameters:</B><DD><CODE>columnData</CODE> - the input column data
<DT><B>Returns:</B><DD>a columnData x 1 FieldMatrix
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if <code>data</code> is empty.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>columnData</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="checkSymmetric(org.apache.commons.math3.linear.RealMatrix, double)"><!-- --></A><H3>
checkSymmetric</H3>
<PRE>
public static void <B>checkSymmetric</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
                                  double&nbsp;eps)</PRE>
<DL>
<DD>Checks whether a matrix is symmetric.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>matrix</CODE> - Matrix to check.<DD><CODE>eps</CODE> - Relative tolerance.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></CODE> - if the matrix is not square.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSymmetricMatrixException.html" title="class in org.apache.commons.math3.linear">NonSymmetricMatrixException</A></CODE> - if the matrix is not symmetric.<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="isSymmetric(org.apache.commons.math3.linear.RealMatrix, double)"><!-- --></A><H3>
isSymmetric</H3>
<PRE>
public static boolean <B>isSymmetric</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
                                  double&nbsp;eps)</PRE>
<DL>
<DD>Checks whether a matrix is symmetric.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>matrix</CODE> - Matrix to check.<DD><CODE>eps</CODE> - Relative tolerance.
<DT><B>Returns:</B><DD><code>true</code> if <code>matrix</code> is symmetric.<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="checkMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int, int)"><!-- --></A><H3>
checkMatrixIndex</H3>
<PRE>
public static void <B>checkMatrixIndex</B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                                    int&nbsp;row,
                                    int&nbsp;column)
                             throws <A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></PRE>
<DL>
<DD>Check if matrix indices are valid.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>m</CODE> - Matrix.<DD><CODE>row</CODE> - Row index to check.<DD><CODE>column</CODE> - Column index to check.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></CODE> - if <code>row</code> or <code>column</code> is not
 a valid index.</DL>
</DD>
</DL>
<HR>

<A NAME="checkRowIndex(org.apache.commons.math3.linear.AnyMatrix, int)"><!-- --></A><H3>
checkRowIndex</H3>
<PRE>
public static void <B>checkRowIndex</B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                                 int&nbsp;row)
                          throws <A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></PRE>
<DL>
<DD>Check if a row index is valid.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>m</CODE> - Matrix.<DD><CODE>row</CODE> - Row index to check.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></CODE> - if <code>row</code> is not a valid index.</DL>
</DD>
</DL>
<HR>

<A NAME="checkColumnIndex(org.apache.commons.math3.linear.AnyMatrix, int)"><!-- --></A><H3>
checkColumnIndex</H3>
<PRE>
public static void <B>checkColumnIndex</B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                                    int&nbsp;column)
                             throws <A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></PRE>
<DL>
<DD>Check if a column index is valid.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>m</CODE> - Matrix.<DD><CODE>column</CODE> - Column index to check.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></CODE> - if <code>column</code> is not a valid index.</DL>
</DD>
</DL>
<HR>

<A NAME="checkSubMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int, int, int, int)"><!-- --></A><H3>
checkSubMatrixIndex</H3>
<PRE>
public static void <B>checkSubMatrixIndex</B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                                       int&nbsp;startRow,
                                       int&nbsp;endRow,
                                       int&nbsp;startColumn,
                                       int&nbsp;endColumn)
                                throws <A HREF="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A>,
                                       <A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></PRE>
<DL>
<DD>Check if submatrix ranges indices are valid.
 Rows and columns are indicated counting from 0 to <code>n - 1</code>.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>m</CODE> - Matrix.<DD><CODE>startRow</CODE> - Initial row index.<DD><CODE>endRow</CODE> - Final row index.<DD><CODE>startColumn</CODE> - Initial column index.<DD><CODE>endColumn</CODE> - Final column index.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></CODE> - if the indices are invalid.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A></CODE> - if <code>endRow &lt; startRow</code> or
 <code>endColumn &lt; startColumn</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="checkSubMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int[], int[])"><!-- --></A><H3>
checkSubMatrixIndex</H3>
<PRE>
public static void <B>checkSubMatrixIndex</B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;m,
                                       int[]&nbsp;selectedRows,
                                       int[]&nbsp;selectedColumns)
                                throws <A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A>,
                                       <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                                       <A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></PRE>
<DL>
<DD>Check if submatrix ranges indices are valid.
 Rows and columns are indicated counting from 0 to n-1.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>m</CODE> - Matrix.<DD><CODE>selectedRows</CODE> - Array of row indices.<DD><CODE>selectedColumns</CODE> - Array of column indices.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>selectedRows</code> or
 <code>selectedColumns</code> are <code>null</code>.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if the row or column selections are empty (zero
 length).
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></CODE> - if row or column selections are not valid.</DL>
</DD>
</DL>
<HR>

<A NAME="checkAdditionCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)"><!-- --></A><H3>
checkAdditionCompatible</H3>
<PRE>
public static void <B>checkAdditionCompatible</B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;left,
                                           <A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;right)
                                    throws <A HREF="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</A></PRE>
<DL>
<DD>Check if matrices are addition compatible.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>left</CODE> - Left hand side matrix.<DD><CODE>right</CODE> - Right hand side matrix.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</A></CODE> - if the matrices are not addition
 compatible.</DL>
</DD>
</DL>
<HR>

<A NAME="checkSubtractionCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)"><!-- --></A><H3>
checkSubtractionCompatible</H3>
<PRE>
public static void <B>checkSubtractionCompatible</B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;left,
                                              <A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;right)
                                       throws <A HREF="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</A></PRE>
<DL>
<DD>Check if matrices are subtraction compatible
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>left</CODE> - Left hand side matrix.<DD><CODE>right</CODE> - Right hand side matrix.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</A></CODE> - if the matrices are not addition
 compatible.</DL>
</DD>
</DL>
<HR>

<A NAME="checkMultiplicationCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)"><!-- --></A><H3>
checkMultiplicationCompatible</H3>
<PRE>
public static void <B>checkMultiplicationCompatible</B>(<A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;left,
                                                 <A HREF="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</A>&nbsp;right)
                                          throws <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></PRE>
<DL>
<DD>Check if matrices are multiplication compatible
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>left</CODE> - Left hand side matrix.<DD><CODE>right</CODE> - Right hand side matrix.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if matrices are not multiplication
 compatible.</DL>
</DD>
</DL>
<HR>

<A NAME="fractionMatrixToRealMatrix(org.apache.commons.math3.linear.FieldMatrix)"><!-- --></A><H3>
fractionMatrixToRealMatrix</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</A> <B>fractionMatrixToRealMatrix</B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/fraction/Fraction.html" title="class in org.apache.commons.math3.fraction">Fraction</A>&gt;&nbsp;m)</PRE>
<DL>
<DD>Convert a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A>/<A HREF="../../../../../org/apache/commons/math3/fraction/Fraction.html" title="class in org.apache.commons.math3.fraction"><CODE>Fraction</CODE></A> matrix to a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>m</CODE> - Matrix to convert.
<DT><B>Returns:</B><DD>the converted matrix.</DL>
</DD>
</DL>
<HR>

<A NAME="bigFractionMatrixToRealMatrix(org.apache.commons.math3.linear.FieldMatrix)"><!-- --></A><H3>
bigFractionMatrixToRealMatrix</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</A> <B>bigFractionMatrixToRealMatrix</B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction">BigFraction</A>&gt;&nbsp;m)</PRE>
<DL>
<DD>Convert a <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>FieldMatrix</CODE></A>/<A HREF="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><CODE>BigFraction</CODE></A> matrix to a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>m</CODE> - Matrix to convert.
<DT><B>Returns:</B><DD>the converted matrix.</DL>
</DD>
</DL>
<HR>

<A NAME="serializeRealVector(org.apache.commons.math3.linear.RealVector, java.io.ObjectOutputStream)"><!-- --></A><H3>
serializeRealVector</H3>
<PRE>
public static void <B>serializeRealVector</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;vector,
                                       <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/ObjectOutputStream.html?is-external=true" title="class or interface in java.io">ObjectOutputStream</A>&nbsp;oos)
                                throws <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></PRE>
<DL>
<DD>Serialize a <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A>.
 <p>
 This method is intended to be called from within a private
 <code>writeObject</code> method (after a call to
 <code>oos.defaultWriteObject()</code>) in a class that has a
 <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> field, which should be declared <code>transient</code>.
 This way, the default handling does not serialize the vector (the <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> interface is not serializable by default) but this method does
 serialize it specifically.
 </p>
 <p>
 The following example shows how a simple class with a name and a real vector
 should be written:
 <pre><code>
 public class NamedVector implements Serializable {

     private final String name;
     private final transient RealVector coefficients;

     // omitted constructors, getters ...

     private void writeObject(ObjectOutputStream oos) throws IOException {
         oos.defaultWriteObject();  // takes care of name field
         MatrixUtils.serializeRealVector(coefficients, oos);
     }

     private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException {
         ois.defaultReadObject();  // takes care of name field
         MatrixUtils.deserializeRealVector(this, "coefficients", ois);
     }

 }
 </code></pre>
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>vector</CODE> - real vector to serialize<DD><CODE>oos</CODE> - stream where the real vector should be written
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></CODE> - if object cannot be written to stream<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#deserializeRealVector(java.lang.Object, java.lang.String, java.io.ObjectInputStream)"><CODE>deserializeRealVector(Object, String, ObjectInputStream)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="deserializeRealVector(java.lang.Object, java.lang.String, java.io.ObjectInputStream)"><!-- --></A><H3>
deserializeRealVector</H3>
<PRE>
public static void <B>deserializeRealVector</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>&nbsp;instance,
                                         <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A>&nbsp;fieldName,
                                         <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/ObjectInputStream.html?is-external=true" title="class or interface in java.io">ObjectInputStream</A>&nbsp;ois)
                                  throws <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/ClassNotFoundException.html?is-external=true" title="class or interface in java.lang">ClassNotFoundException</A>,
                                         <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></PRE>
<DL>
<DD>Deserialize  a <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> field in a class.
 <p>
 This method is intended to be called from within a private
 <code>readObject</code> method (after a call to
 <code>ois.defaultReadObject()</code>) in a class that has a
 <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> field, which should be declared <code>transient</code>.
 This way, the default handling does not deserialize the vector (the <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> interface is not serializable by default) but this method does
 deserialize it specifically.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>instance</CODE> - instance in which the field must be set up<DD><CODE>fieldName</CODE> - name of the field within the class (may be private and final)<DD><CODE>ois</CODE> - stream from which the real vector should be read
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/ClassNotFoundException.html?is-external=true" title="class or interface in java.lang">ClassNotFoundException</A></CODE> - if a class in the stream cannot be found
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></CODE> - if object cannot be read from the stream<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#serializeRealVector(org.apache.commons.math3.linear.RealVector, java.io.ObjectOutputStream)"><CODE>serializeRealVector(RealVector, ObjectOutputStream)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="serializeRealMatrix(org.apache.commons.math3.linear.RealMatrix, java.io.ObjectOutputStream)"><!-- --></A><H3>
serializeRealMatrix</H3>
<PRE>
public static void <B>serializeRealMatrix</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
                                       <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/ObjectOutputStream.html?is-external=true" title="class or interface in java.io">ObjectOutputStream</A>&nbsp;oos)
                                throws <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></PRE>
<DL>
<DD>Serialize a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.
 <p>
 This method is intended to be called from within a private
 <code>writeObject</code> method (after a call to
 <code>oos.defaultWriteObject()</code>) in a class that has a
 <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> field, which should be declared <code>transient</code>.
 This way, the default handling does not serialize the matrix (the <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> interface is not serializable by default) but this method does
 serialize it specifically.
 </p>
 <p>
 The following example shows how a simple class with a name and a real matrix
 should be written:
 <pre><code>
 public class NamedMatrix implements Serializable {

     private final String name;
     private final transient RealMatrix coefficients;

     // omitted constructors, getters ...

     private void writeObject(ObjectOutputStream oos) throws IOException {
         oos.defaultWriteObject();  // takes care of name field
         MatrixUtils.serializeRealMatrix(coefficients, oos);
     }

     private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException {
         ois.defaultReadObject();  // takes care of name field
         MatrixUtils.deserializeRealMatrix(this, "coefficients", ois);
     }

 }
 </code></pre>
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>matrix</CODE> - real matrix to serialize<DD><CODE>oos</CODE> - stream where the real matrix should be written
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></CODE> - if object cannot be written to stream<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#deserializeRealMatrix(java.lang.Object, java.lang.String, java.io.ObjectInputStream)"><CODE>deserializeRealMatrix(Object, String, ObjectInputStream)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="deserializeRealMatrix(java.lang.Object, java.lang.String, java.io.ObjectInputStream)"><!-- --></A><H3>
deserializeRealMatrix</H3>
<PRE>
public static void <B>deserializeRealMatrix</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>&nbsp;instance,
                                         <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A>&nbsp;fieldName,
                                         <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/ObjectInputStream.html?is-external=true" title="class or interface in java.io">ObjectInputStream</A>&nbsp;ois)
                                  throws <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/ClassNotFoundException.html?is-external=true" title="class or interface in java.lang">ClassNotFoundException</A>,
                                         <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></PRE>
<DL>
<DD>Deserialize  a <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> field in a class.
 <p>
 This method is intended to be called from within a private
 <code>readObject</code> method (after a call to
 <code>ois.defaultReadObject()</code>) in a class that has a
 <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> field, which should be declared <code>transient</code>.
 This way, the default handling does not deserialize the matrix (the <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A> interface is not serializable by default) but this method does
 deserialize it specifically.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>instance</CODE> - instance in which the field must be set up<DD><CODE>fieldName</CODE> - name of the field within the class (may be private and final)<DD><CODE>ois</CODE> - stream from which the real matrix should be read
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/ClassNotFoundException.html?is-external=true" title="class or interface in java.lang">ClassNotFoundException</A></CODE> - if a class in the stream cannot be found
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></CODE> - if object cannot be read from the stream<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#serializeRealMatrix(org.apache.commons.math3.linear.RealMatrix, java.io.ObjectOutputStream)"><CODE>serializeRealMatrix(RealMatrix, ObjectOutputStream)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="solveLowerTriangularSystem(org.apache.commons.math3.linear.RealMatrix, org.apache.commons.math3.linear.RealVector)"><!-- --></A><H3>
solveLowerTriangularSystem</H3>
<PRE>
public static void <B>solveLowerTriangularSystem</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;rm,
                                              <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b)
                                       throws <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                                              <A HREF="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</A>,
                                              <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></PRE>
<DL>
<DD>Solve  a  system of composed of a Lower Triangular Matrix
 <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.
 <p>
 This method is called to solve systems of equations which are
 of the lower triangular form. The matrix <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>
 is assumed, though not checked, to be in lower triangular form.
 The vector <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> is overwritten with the solution.
 The matrix is checked that it is square and its dimensions match
 the length of the vector.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>rm</CODE> - RealMatrix which is lower triangular<DD><CODE>b</CODE> - RealVector this is overwritten
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the matrix and vector are not
 conformable
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></CODE> - if the matrix <code>rm</code> is not square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</A></CODE> - if the absolute value of one of the diagonal
 coefficient of <code>rm</code> is lower than <A HREF="../../../../../org/apache/commons/math3/util/Precision.html#SAFE_MIN"><CODE>Precision.SAFE_MIN</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="solveUpperTriangularSystem(org.apache.commons.math3.linear.RealMatrix, org.apache.commons.math3.linear.RealVector)"><!-- --></A><H3>
solveUpperTriangularSystem</H3>
<PRE>
public static void <B>solveUpperTriangularSystem</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;rm,
                                              <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b)
                                       throws <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                                              <A HREF="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</A>,
                                              <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></PRE>
<DL>
<DD>Solver a  system composed  of an Upper Triangular Matrix
 <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>.
 <p>
 This method is called to solve systems of equations which are
 of the lower triangular form. The matrix <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><CODE>RealMatrix</CODE></A>
 is assumed, though not checked, to be in upper triangular form.
 The vector <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><CODE>RealVector</CODE></A> is overwritten with the solution.
 The matrix is checked that it is square and its dimensions match
 the length of the vector.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>rm</CODE> - RealMatrix which is upper triangular<DD><CODE>b</CODE> - RealVector this is overwritten
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the matrix and vector are not
 conformable
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></CODE> - if the matrix <code>rm</code> is not
 square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</A></CODE> - if the absolute value of one of the diagonal
 coefficient of <code>rm</code> is lower than <A HREF="../../../../../org/apache/commons/math3/util/Precision.html#SAFE_MIN"><CODE>Precision.SAFE_MIN</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="blockInverse(org.apache.commons.math3.linear.RealMatrix, int)"><!-- --></A><H3>
blockInverse</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>blockInverse</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;m,
                                      int&nbsp;splitIndex)</PRE>
<DL>
<DD>Computes the inverse of the given matrix by splitting it into
 4 sub-matrices.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>m</CODE> - Matrix whose inverse must be computed.<DD><CODE>splitIndex</CODE> - Index that determines the "split" line and
 column.
 The element corresponding to this index will part of the
 upper-left sub-matrix.
<DT><B>Returns:</B><DD>the inverse of <code>m</code>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></CODE> - if <code>m</code> is not square.</DL>
</DD>
</DL>
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